So I need to buy a new phone definitely. I currently have the Google Nexus 3 (Samsung one) but am giving that to my mom when I go back to India a the end of December.
So first thing first is I need a new phone. Now, I don't want the Apple iPhone at all. I'm willing to go with Android and I'm even willing to switch to WP8. I need the phone unlocked though so I can use it all around the world.

After that, I need to buy a new laptop too but I was thinking of a laptop/tablet hybrid or a laptop + tablet combination.

Budget for phone: Up to $700 (full price but hopefully less)
Budget for laptop/tablet (or both!): Up to $2,000 but hopefully way less.

Lumia 920? I don't know, what are you looking for in a phone? I would choose it cos I love WP7 and WP8 seems to be the same only better. And also cos I love the design and build quality on the 800. But yeah...

As for tablet/laptop... nowadays tablets aren't much laptop replacements, but seems that might change with the Surface Pro. I'm sorry, I'm not totally in the loop laptops-wise, so I can't recommend you a specific brand/model. I can tell you that if I was to get one now I'd go for an ultrabook. They seem to have a good balance between performance and portability and, while expensive, they're not terribly so. I think any of them will be for sure under 2000. Where are you now, by the way?

Not sure about the latest Android smartphones, ie. SIII - but I know the Lumia 710 at least (I'd imagine the rest of the Lumia range would follow suit) require a MicroSIM, so if you are needing it unlocked to use in other countries, I'd check you can buy MicroSIM cards for those operators

Although a tip: I bought the Lumia 710 and didn't realise I needed the MicroSIM, so took a chance and cut the chip out of the normal SIMCard to the size of a MicroSIM and it worked 100%, so basically the MicroSIM is the same as a normal SIM minus the plastic surround

Not sure about the latest Android smartphones, ie. SIII - but I know the Lumia 710 at least (I'd imagine the rest of the Lumia range would follow suit) require a MicroSIM, so if you are needing it unlocked to use in other countries, I'd check you can buy MicroSIM cards for those operators

Although a tip: I bought the Lumia 710 and didn't realise I needed the MicroSIM, so took a chance and cut the chip out of the normal SIMCard to the size of a MicroSIM and it worked 100%, so basically the MicroSIM is the same as a normal SIM minus the plastic surround

Exactly. Most phone stores have SIM-cutters that just push out a microSIM in a second.

For a tablet get an iPad. No other tablet OS has the same app ecosystem. If you're not interested in that get a Nexus 10. Again, incredible tablet with great hardware at a low price, and you'll be able to re-use any app purchases from your Android phone.

Laptop? Depends on what you need. The Sony Vaio T 13" is a great ultrabook for a low price and it has a great touchscreen to benifit from Windows 8 fully. If that's too small/not powerful enough consider the Vaio S-series. 13" and 15", really good specs, thin, light, long battery life and a dedicated GPU at a good price.

I'm in New York right now. Going back to India on the 21st of December so have to buy before that.

Phone wise, Android or WP8 is a go. I'm kinda torn right now. As much as I love the Android ecosystem, I love the look and feel of WP8 and feel the apps are only going to get better sooner rather than later.

Laptop/Tablet: I was asking if I should buy both or just buy a laptop. I do not want an iPad at all. Don't like it. I need something portable but with enough oomph to play some games like Call of Duty, FIFA and NFS.